The only .tmp files that I've seen excel make are in that windows temp folder.
When I opened a test workbook, I saw my temp folder get filled with:
C:\WINDOWS\TEMP\~DF2F53.TMP
C:\WINDOWS\TEMP\~DF3038.TMP
C:\WINDOWS\TEMP\~DF338E.TMP
C:\WINDOWS\TEMP\~DF344F.TMP
C:\WINDOWS\TEMP\~DF3452.TMP
C:\WINDOWS\TEMP\~DF34A1.TMP
C:\WINDOWS\TEMP\~DF486B.TMP
C:\WINDOWS\TEMP\C2D1.TMP
C:\WINDOWS\TEMP\C2E2.TMP
C:\WINDOWS\TEMP\mflC314.TMP
C:\WINDOWS\TEMP\VBE
Do your .tmp files have the same kind of names.
Any chance that you have some code creating these (not excel by itself)?
If you close excel, delete the .tmp files, and reopen excel in safe mode:
Windows start button
run
excel /safe
(Safe mode will disable lots of stuff--including macros.)
And then open that workbook, do you still get those temp files?
And when I close excel, it usually (not always) cleans up these .tmp files.
(but it does leave the VBE folder.)